DELHI—The Yamuna River that flows through this ancient city has helped sustain some of India’s greatest empires. Hindu poets celebrated its life-giving properties. The Mughal dynasty built the Taj Mahal and other monuments along its banks.

Today, the Yamuna is a foul sludge for much of its 855-mile run. In Delhi, it is black and nearly motionless, covered in many areas with a foam of industrial chemicals, floating plastic and human waste.